What does it mean for something to be "logically possible"?

[bilby]

Untermensche, you are so painfully wrong about "logically possible", but maybe that doesn't matter to you. For something to be "logically possible", it only has to pass the test of the  law of noncontradiction. Claims that pass that test in imaginary realities are therefore logically possible. There is nothing about the concept that requires it to be consistent with the model that we believe to be most plausible at any particular point in time.

I am entitled to my opinions.

No, you are not. Not in the context of a discussion in the Logic and Epistemology forum.

I’m sure you’ve heard the expression ‘everyone is entitled to their opinion.’ Perhaps you’ve even said it yourself, maybe to head off an argument or bring one to a close. Well, as soon as you walk into this room, it’s no longer true. You are not entitled to your opinion. You are only entitled to what you can argue for.

https://theconversation.com/no-youre-not-entitled-to-your-opinion-9978

I'm entitled to my opinion or I have a right to my opinion is a logical fallacy in which a person discredits any opposition by claiming that they are entitled to their opinion. The statement exemplifies a red herring. Whether one has a particular entitlement or right is irrelevant to whether one's assertion is true or false. To assert the existence of the right is a failure to assert any justification for the opinion.

 

[untermensche]

I am entitled to my opinions.

No, you are not. Not in the context of a discussion in the Logic and Epistemology forum.

https://theconversation.com/no-youre-not-entitled-to-your-opinion-9978

I'm entitled to my opinion or I have a right to my opinion is a logical fallacy in which a person discredits any opposition by claiming that they are entitled to their opinion. The statement exemplifies a red herring. Whether one has a particular entitlement or right is irrelevant to whether one's assertion is true or false. To assert the existence of the right is a failure to assert any justification for the opinion.

Yes I am.

Even in a precious Logic and Epistemology forum.

If I claim my opinions have validity because they are my opinions I have committed a fallacy.

But I wasn't doing that.

I was just setting up my question, which was my salient point.

But you focused on the throw away set up, not my point. You focus on trivial nonsense, not ideas.

 

[bilby]

No, you are not. Not in the context of a discussion in the Logic and Epistemology forum.

https://theconversation.com/no-youre-not-entitled-to-your-opinion-9978

I'm entitled to my opinion or I have a right to my opinion is a logical fallacy in which a person discredits any opposition by claiming that they are entitled to their opinion. The statement exemplifies a red herring. Whether one has a particular entitlement or right is irrelevant to whether one's assertion is true or false. To assert the existence of the right is a failure to assert any justification for the opinion.

Yes I am.

Even in a precious Logic and Epistemology forum.

If I claim my opinions have validity because they are my opinions I have committed a fallacy.

But I wasn't doing that.

I was just setting up my question, which was my salient point.

But you focused on the throw away set up, not my point. You focus on trivial nonsense, not ideas.

Nice backpedalling; But sadly, this is an Internet forum - everyone can read back and confirm exactly what you wrote.

And a question isn't a point. Which is really something you should know, before attempting to have any discussion about logic.

 

[untermensche]

No, you are not. Not in the context of a discussion in the Logic and Epistemology forum.

https://theconversation.com/no-youre-not-entitled-to-your-opinion-9978

I'm entitled to my opinion or I have a right to my opinion is a logical fallacy in which a person discredits any opposition by claiming that they are entitled to their opinion. The statement exemplifies a red herring. Whether one has a particular entitlement or right is irrelevant to whether one's assertion is true or false. To assert the existence of the right is a failure to assert any justification for the opinion.

Yes I am.

Even in a precious Logic and Epistemology forum.

If I claim my opinions have validity because they are my opinions I have committed a fallacy.

But I wasn't doing that.

I was just setting up my question, which was my salient point.

But you focused on the throw away set up, not my point. You focus on trivial nonsense, not ideas.

Nice backpedalling; But sadly, this is an Internet forum - everyone can read back and confirm exactly what you wrote.

And a question isn't a point. Which is really something you should know, before attempting to have any discussion about logic.

The two people that care don't care about your pettiness.

The person said:

For something to be "logically possible", it only has to pass the test of the law of noncontradiction.

So I asked:

If a human can jump 1 foot high is it logically possible they can jump 100?

I don't see any contradiction.

But please blather on about my being allowed to express my opinions.

 

[Copernicus]

Untermensche, you are so painfully wrong about "logically possible", but maybe that doesn't matter to you. For something to be "logically possible", it only has to pass the test of the  law of noncontradiction. Claims that pass that test in imaginary realities are therefore logically possible. There is nothing about the concept that requires it to be consistent with the model that we believe to be most plausible at any particular point in time.

I am entitled to my opinions.

Yes, but that is true of everyone, including dogmatists and fanatics. I would not say that you aren't entitled to your opinions. Whether you can make them sound plausible to other reasonable people is what is at issue here.

If a human can jump 1 foot high is it logically possible they can jump 100?

Absolutely. You seem to consistently confuse logically possible with merely plausible. That is the problem with your opinion.

 

[untermensche]

I am entitled to my opinions.

Yes, but that is true of everyone, including dogmatists and fanatics. I would not say that you aren't entitled to your opinions. Whether you can make them sound plausible to other reasonable people is what is at issue here.

If a human can jump 1 foot high is it logically possible they can jump 100?

Absolutely. You seem to consistently confuse logically possible with merely plausible. That is the problem with your opinion.

So you think someday a person may jump 100 feet because a person jumped 1 foot? On earth?

Absurd.

There is nothing logical about that.

 

[Bomb#20]

I don't know if the number is finite or infinite. No human knows.

You do know that infinity is not a number. It is a concept. The concept of limitlessness of numbers without end.

I didn't say infinity is a number. "Infinite" is a property of some numbers and not of others. You might as well respond to my using the concept "even number" by lecturing me that "Even is not a number."

Aleph-null is a number; it's the smallest infinite number. The number of atoms in the universe might be finite, or it might be aleph-null. It undoubtedly is not 2^aleph-null, which is a larger infinite number than aleph-null.

Can there be something real that is limitless?

"Can"? That's just another word for "possible". It's underspecified. Do you mean "Is it logically possible for something to be real and limitless?"? If so, yes, since there's no proof to the contrary. Or do you mean "Is it physically possible for something to be real and limitless?"? That, we don't know. The laws of physics might conflict with real things being limitless, or they might not. We do not yet know all the laws of physics.

Not uncountable, actually without limit?

How would that work?

Depends on which real thing is limitless. If the number of atoms is limitless, that works by the universe not having large-scale positive curvature and not having walls.

If the future and the past are limitless, that works by conservation of energy.

If the number of points between any two points is limitless, that works by the laws of physics being differential equations. You can't have a derivative if you don't have a dense point set.

Your turn. Suppose nothing real is limitless. That would imply position and age are discrete, not continuous. How would that work? Can you show us some possible formulas for gravity, electromagnetism and nuclear forces that treat position and age as discrete, and still predict observations as accurately as GR and the Standard Model?

 

[untermensche]

You do know that infinity is not a number. It is a concept. The concept of limitlessness of numbers without end.

I didn't say infinity is a number. "Infinite" is a property of some numbers and not of others.

What numbers have the property of infinity? Which ones? Not group of numbers, the specific numbers that have the property of infinity.

Adding infinity to a group just makes it an imaginary group. It changes it from something real to something imaginary. Something that goes on forever. A thing that only exists in the imagination.

Aleph-null is a number; it's the smallest infinite number.

Not a number. A concept. The concept of "the smallest".

Which number is it?

"Is it logically possible for something to be real and limitless?"? If so, yes, since there's no proof to the contrary.

Asking for proof requires showing it is a rational statement.

It requires proving the concept of "limitless" is something possible.

If it is purely imaginary then trying to apply it to real things is illogical.

Like asking if it is logically possible for something to be real and dimensionless?

 

[Bomb#20]

I didn't say infinity is a number. "Infinite" is a property of some numbers and not of others.

What numbers have the property of infinity? Which ones? Not group of numbers, the specific numbers that have the property of infinity.

aleph-null, 2^aleph-null, 2^2aleph-null, ..., and also infinitely many others that are harder to describe. Pretty much any infinite number you'd encounter outside of a math course on transfinites is one of the first few in that list. aleph-null is the number of integers. 2^aleph-null is the number of real numbers. 2^2aleph-null is the number of possible functions of real numbers.

Adding infinity to a group just makes it an imaginary group. It changes it from something real to something imaginary. Something that goes on forever. A thing that only exists in the imagination.

The same has been said every time we expanded our understanding of what a number is. Negative numbers were declared not to be real. Then the square root of 2 was declared not to be real. Then the square root of -1 was declared not to be real -- that was so recent we still label it an "imaginary number".

Aleph-null is a number; it's the smallest infinite number.

Not a number. A concept. The concept of "the smallest".

Which number is it?

It's aleph-null. You might as well ask which number 0 is? It's 0. What other kind of answer do you think you ever get when you ask what number a number is?

1, 0, -1, 3/5, sqrt(2), i, and aleph-null are all concepts; they're all numbers; they're all equally real. When you reject the discoveries of 19th-century math, how the heck are you being different from the fools who rejected the discoveries of 16th-century math and insisted x² + 1 = 0 simply had no solution?

"Is it logically possible for something to be real and limitless?"? If so, yes, since there's no proof to the contrary.

Asking for proof requires showing it is a rational statement.

It requires proving the concept of "limitless" is something possible.

All sorts of things are possible that aren't rational statements. It's possible that my cat is dead; but I saw him ten minutes ago, and he seemed fine, so it would be completely irrational for me to state "My cat is dead.".

If it is purely imaginary then trying to apply it to real things is illogical.

Like asking if it is logically possible for something to be real and dimensionless?

Of course that's logically possible. What dimensions things have is a matter for physics and physical law. The laws of physics could have been different. The universe didn't have to have dimensions at all. Seriously, dude, why did you specify "logically possible" in the title of your thread if you weren't prepared to distinguish between "logically possible" and "physically possible"?

 

[fast]

Let's say I'm a darn good basketball player and can make shots in the hoop from center court (if I can see the basket). If you build a wall two feet taller than myself, it's both physically possible and logically possible for me to make the shot, as I can jump up two feet off the ground, see the basket, and make the shot. If you build the wall twenty feet high, it's physically impossible for me to jump that high (unaided by any artificial device), yet although it's physically impossible to make the shot (given the physical limitations), it's not logically impossible to make the shot, for if (if, I say) I could make the jump, there's no alternate reason for why the shot couldn't be made.

The whole point (well, at least the point I'm putting forward) of expanding the scope of possibility beyond physical possibilities is to show the logic of what could be done given alternate scenarios. Nowhere was it ever intended for logical possibilities to be confined to true physical possibilities.

Never mind all this imaginary stuff. If I could, not that I can, but IF (IF, I say) I could make the jump IN THE REAL WORLD (not some jibe about imaginations), then (THEN) I could make the shot.

You deny that it's logically possible because never could it be physically possible (on Earth with regular gravitation and without aid of some sort)?

Since a basketball shot is more than something imaginary a basketball shot is possible.

Whether one can actually make the shot or not depends on many things.

But the shot itself is not something imaginary.

What about the jump? It's not possible (not physically possible, that is), and with no jump, no shot.

 

[untermensche]

What numbers have the property of infinity? Which ones? Not group of numbers, the specific numbers that have the property of infinity.

aleph-null, 2^aleph-null, 2^2aleph-null, ..., and also infinitely many others that are harder to describe. Pretty much any infinite number you'd encounter outside of a math course on transfinites is one of the first few in that list. aleph-null is the number of integers. 2^aleph-null is the number of real numbers. 2^2aleph-null is the number of possible functions of real numbers.

Infinity is not simply a number. It is number plus some other imaginary conception added on, like "without end" or "without beginning".

Trying to find infinity in nature is like trying to find the number "three" in nature. It is not there.

They are both imaginary conceptions that have no real world existence. And there is no reason to think they could have a real world existence.

It's aleph-null. You might as well ask which number 0 is? It's 0.

Not merely numbers. Conceptions on top of the conception of number. Zero is the conception of "without number" or "without value".

All sorts of things are possible that aren't rational statements. It's possible that my cat is dead; but I saw him ten minutes ago, and he seemed fine, so it would be completely irrational for me to state "My cat is dead.".

You're defining "rational" as expressing the truth.

That is "truthful", not "rational".

Is it rational to express the truth? Not always.

Like asking if it is logically possible for something to be real and dimensionless?

Of course that's logically possible.

Then give some logic showing how it is possible.

Not some empty claim about how dimensions are not necessary.

 

[Copernicus]

Yes, but that is true of everyone, including dogmatists and fanatics. I would not say that you aren't entitled to your opinions. Whether you can make them sound plausible to other reasonable people is what is at issue here.

If a human can jump 1 foot high is it logically possible they can jump 100?

Absolutely. You seem to consistently confuse logically possible with merely plausible. That is the problem with your opinion.

So you think someday a person may jump 100 feet because a person jumped 1 foot? On earth?

Don't be obtuse. I said nothing of the sort.

Absurd.

There is nothing logical about that.

Right here is the source of your misunderstanding of logic. Absurd claims can be logically possible claims. Logic is about truth consistency, not necessarily what is true in reality. That is why logicians make a distinction between validity and soundness.

 

[untermensche]

What about the jump? It's not possible (not physically possible, that is), and with no jump, no shot.

Then you are talking about physical impossibility, not logical.

To say physical impossibilities are possible is just a lie, not irrational.

It is not always irrational to lie.

 

[untermensche]

So you think someday a person may jump 100 feet because a person jumped 1 foot? On earth?

Don't be obtuse. I said nothing of the sort.

I asked: If a human can jump 1 foot high is it logically possible they can jump 100?

And you answered:

Absolutely.

You clearly say it is logically possible for some event to take place.

If it is logically possible it must be physically possible as well.

It is not logic to say things are possible if they are not physically possible.

Absurd claims can be logically possible claims.

Like what?

 

[ryan]

Absurd claims can be logically possible claims.

Like what?

Using scientific laws and theories as premises, it is logically possible for a teapot to be orbiting Jupiter.

 

[untermensche]

Like what?

Using scientific laws and theories as premises, it is logically possible for a teapot to be orbiting Jupiter.

Is it?

What laws put it there?

 

[ryan]

Using scientific laws and theories as premises, it is logically possible for a teapot to be orbiting Jupiter.

Is it?

What laws put it there?

Are you seriously asking what laws would enable a teapot to get to Jupiter? You know enough physics to know that our physical laws allow a teapot to get to Jupiter's orbit.

 

[Copernicus]

Don't be obtuse. I said nothing of the sort.

I asked: If a human can jump 1 foot high is it logically possible they can jump 100?

And you answered:

Absolutely.

You clearly say it is logically possible for some event to take place.

If it is logically possible it must be physically possible as well.

It is not logic to say things are possible if they are not physically possible.

On the off-chance that you still don't quite grasp my point but are willing to consider its possibility, I'll try to explain it again. If we assume that gravity suddenly weakens to the point where a man can jump 100 feet or that the man is standing on a celestial body with weak gravity, then it would be valid to claim that a human can physically jump 100 feet. There are many other assumptions that would lead to that valid conclusion. So that certainly makes the claim logically possible, even though it is a highly implausible claim to make, given our practical knowledge of the circumstances. Just use your imagination.

Absurd claims can be logically possible claims.

Like what?

Your 100 foot claim.

 

[fast]

What about the jump? It's not possible (not physically possible, that is), and with no jump, no shot.

Then you are talking about physical impossibility, not logical.

To say physical impossibilities are possible is just a lie, not irrational.

It is not always irrational to lie.

Many physical impossibilities are possible. The jump is an example.

The jump is a physical impossibility, but it would be inaccurate to conclude that the jump is therefore impossible.

Edited to add:

Because the jump is physically impossible, it cannot be true that the jump is also physically possible.

Editing to add more:

Every physically possible event is logically possible, but not every logically possible event is physically possible. Many logically possible events are physically impossible (like the jump).

 

[beero1000]

aleph-null, 2^aleph-null, 2^2aleph-null, ..., and also infinitely many others that are harder to describe. Pretty much any infinite number you'd encounter outside of a math course on transfinites is one of the first few in that list. aleph-null is the number of integers. 2^aleph-null is the number of real numbers. 2^2aleph-null is the number of possible functions of real numbers.

Infinity is not simply a number. It is number plus some other imaginary conception added on, like "without end" or "without beginning".

Trying to find infinity in nature is like trying to find the number "three" in nature. It is not there.

They are both imaginary conceptions that have no real world existence. And there is no reason to think they could have a real world existence.

It's aleph-null. You might as well ask which number 0 is? It's 0.

Not merely numbers. Conceptions on top of the conception of number. Zero is the conception of "without number" or "without value".

All sorts of things are possible that aren't rational statements. It's possible that my cat is dead; but I saw him ten minutes ago, and he seemed fine, so it would be completely irrational for me to state "My cat is dead.".

You're defining "rational" as expressing the truth.

That is "truthful", not "rational".

Is it rational to express the truth? Not always.

Like asking if it is logically possible for something to be real and dimensionless?

Of course that's logically possible.

Then give some logic showing how it is possible.

Not some empty claim about how dimensions are not necessary.

You're embarrassing yourself with your ignorance. Seriously, look up "number" in the dictionary.